A new formalism for quantum functional sensitivity analysis (QFSA) of atom-diatom reactions in the gas phase is developed within a version of Manolopoulos et al.’s [J. Chem. Phys. 93, 403 (1990)] log-derivative Kohn variational method containing contracted translational basis functions. A reference energy, E(mid), is introduced to define boundary translational functions which completely remove all scattering energy dependence from the basis functions. This greatly facilitates scattering calculations for a range of energies about E(mid) without having to recalculate any of the so-called "stiffness" matrix elements. Our new approach to QFSA is applied to study the sensitivity of the H+H-2, D+H-2, and H+D-2 reaction probabilities to the Boothroyd-Keogh-Martin-Peterson (BKMP) potential energy surface. The transition probability sensitivities of both D+H-2 and H+D-2 are very similar to those of H+H-2 at low energies, but at higher energies, the sensitivities of the H+D-2 reaction differ from those of the other two isotopomers. Isotopomers that have very similar reaction probability profiles also have very similar sensitivities to the potential. All three isotopomers exhibit a large region of positive sensitivity at the top of the barrier for an approximately 0.1 to 0.2 eV energy range above threshold. For these energies (similar to 0.3 to 0.5 eV above the barrier), it is possible to increase the reaction probability with slight increases in barrier height. Sensitivity results from our new code have also provided a wealth of information about (i) how small, localized changes in the potential affect product state distributions, resonance features, and reactivity; and (ii) where the dynamics is most sensitive to inaccuracies in the potential. Comparisons are also made of transition probabilities and sensitivities on the BKMP surface to those of other potential energy surfaces.